integral from 2x to 2 of (x-y)

Lösung

\int_{2 x}^{2} (x - y) d y

2 x - 2

Schritte zur Lösung

\int_{2 x}^{2} x - y d y

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{2 x}^{2} x d y - \int_{2 x}^{2} y d y

\int_{2 x}^{2} x d y = x \cdot 2 - 2 x^{2}

\int_{2 x}^{2} y d y = 2 - 2 x^{2}

= x \cdot 2 - 2 x^{2} - (2 - 2 x^{2})

Vereinfache

x \cdot 2 - 2 x^{2} - (2 - 2 x^{2}) : 2 x - 2

= 2 x - 2

\int_{0}^{3} x^{2} - x - 3 d x

\int_{x}^{1} \frac{1}{x} d x

\int_{0}^{2} 8 \cdot 2^{- x} - 2 d x

\int_{- 1}^{1} (∣ x ∣ - \frac{1}{2})^{2} d x

\int_{0}^{20} (840 - 42 x) d x